ODE No. 1179

\[ \left (a^2 x^2+2\right ) y(x)+x^2 y''(x)-2 x y'(x)=0 \]

✓ Mathematica : cpu = 0.0197277 (sec), leaf count = 38

DSolve[(2 + a^2*x^2)*y[x] - 2*x*Derivative[1][y][x] + x^2*Derivative[2][y][x] == 0,y[x],x]

\[\left \{\left \{y(x)\to c_1 x e^{-i a x}-\frac {i c_2 x e^{i a x}}{2 a}\right \}\right \}\]

✓ Maple : cpu = 0.043 (sec), leaf count = 19

dsolve(x^2*diff(diff(y(x),x),x)-2*x*diff(y(x),x)+(a^2*x^2+2)*y(x)=0,y(x))

\[y \left (x \right ) = x \left (\cos \left (a x \right ) c_{2} +\sin \left (a x \right ) c_{1} \right )\]